Finite Group Databasebeta

← #22619767

Subgroups — #22619767

Order 9344.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989064C211yesmaximal, characteristic
2#17988891C212yesmaximal, complemented
3#17988891C212yesmaximal, complemented
4#17988879C212yesmaximal, complemented
5#17988869C212yesmaximal, complemented
6#17988627C211yesmaximal, characteristic
7#17988623C211yesmaximal, characteristic
8#17988614C211yesmaximal, characteristic
9#17988595C211yesmaximal, characteristic
10C2×#14556514C211yesmaximal, characteristic
11#544×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15C4×Dic146C2212yes—
16C4×Dic146C2212yes—
17#14556556—21no—
18#14556556—21no—
19#14556550C2211yescharacteristic
20#14556547—22no—
21#14556524C2211yescharacteristic
22#14556524C2211yescharacteristic
23#14556524C2212yes—
24#14556522C2211yescharacteristic
25#14556522C2212yes—
26#14556522C2211yescharacteristic
27C4⋊#10596831C2212yes—
28C4⋊#10596831C2212yes—
29#14556514C2212yes—
30#14556514C2212yes—
31#14556514C2212yes—
32#14556514C2212yes—
33C4⋊Q8×C73—21no—
34C4⋊Q8×C73C2212yes—
35#125×C73—21no—
36#125×C73C2212yes—
37C22⋊Q8×C73—22no—
38#117×C73C2211yescharacteristic
39#117×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—22no—
43C2×Dic146Q814yescomplemented
44C2×Dic146C2312yes—
45C22×Dic73—21no—
46#11924012—22no—
47C2×#10596831—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2312yes—
50C2×#10596831C2311yescharacteristic
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73—21no—
56C4×Dic73—22no—
57C4×Dic73—22no—
58C4×Dic73—21no—
59C2×Q8×C73—22no—
60C22×C4×C73—21no—
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—21no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73D411yescharacteristic
67C4⋊C4×C73D411yescharacteristic
68C4⋊C4×C73C2312yes—
69C4⋊C4×C73C2311yescharacteristic
70C4⋊C4×C73C2311yescharacteristic
71C22⋊C4×C73—21no—
72C22⋊C4×C73D412yes—
73C42×C73—21no—
74C42×C73C2312yes—
75C23×C73C2×D411yescharacteristic
76Q8×C73—82no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—81no—
81C2×C4×C73C2×D412yes—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×Q812yes—
85C2×C4×C73#4112yes—
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—24no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91Dic146—24no—
92Dic146—22no—
93Dic146C2×Q814yes—
94#10596831—21no—
95#10596831—21no—
96#10596831—22no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73C22⋊Q812yes—
100C22×C73C22×D411yescharacteristic
101C4×C73—22no—
102C4×C73—22no—
103C4×C73—42no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73C22⋊Q812yes—
107C4×C73C22×Q811yescharacteristic
108C4×C73C2×#4111yescharacteristic
109Dic73—24no—
110Dic73—41no—
111Dic73—41no—
112C2×C73—22no—
113C2×C73C2×C22⋊Q811yescharacteristic
114C2×C73#57711yescharacteristic
115C2×C73#57811yescharacteristic
116#3082—731nomaximal, Sylow
117C73#308211yescharacteristic, complemented, Sylow
118#544D7311yescharacteristic
119#519—731no—
120#479—732no—
121#479—732no—
122#477—732no—
123#475—732no—
124#428—731no—
125#427—731no—
126#424—731no—
127#419—731no—
128C2×#103—731no—
129C22×Q8—731no—
130C2×M16—731no—
131C22×C8—731no—
132C4⋊Q8—21no—
133C4⋊Q8C2×D7312yes—
134#125—21no—
135#125C2×D7312yes—
136C22⋊Q8—22no—
137C4×Q8—732no—
138C4×Q8—732no—
139C4×Q8—1461no—
140C4×Q8—1461no—
141#117—731no—
142#117—1462no—
143#117C2×D7311yescharacteristic
144#117C2×D7311yescharacteristic
145C2×C4⋊C4C2×D7311yescharacteristic
146#107—731no—
147#107—731no—
148#107—732no—
149#106—731no—
150#106—731no—
151#106—732no—
152C4⋊C8—732no—
153C4⋊C8—732no—
154#103—732no—
155#103—732no—
156#103—732no—
157#103—732no—
158C2×Q8—22no—
159C2×Q8—734no—
160C2×Q8—732no—
161C2×Q8—1461no—
162C2×Q8—1462no—
163C22×C4—21no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166M16—1462no—
167C2×C8—731no—
168C2×C8—732no—
169C2×C8—731no—
170C2×C8—1462no—
171C4⋊C4—21no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—731no—
176C4⋊C4—731no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4C22⋊D7311yescharacteristic
180C4⋊C4C22⋊D7311yescharacteristic
181C4⋊C4C22×D7312yes—
182C4⋊C4C22×D7311yescharacteristic
183C4⋊C4C22×D7311yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—1461no—
186C22⋊C4C22⋊D7312yes—
187C42—21no—
188C42—1461no—
189C42—1462no—
190C42—1462no—
191C42C22×D7312yes—
192C23C2×C22⋊D7311yescharacteristic
193Q8—82no—
194Q8—734no—
195Q8—1464no—
196Q8—1462no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1464no—
204C2×C4—1462no—
205C2×C4C2×C22⋊D7312yes—
206C2×C4C2×C22⋊D7312yes—
207C2×C4C2×C22⋊D7311yescharacteristic
208C2×C4Q8×D7312yes—
209C2×C4#1192402912yes—
210C2×C4C23×D7311yescharacteristic
211C8—1461no—
212C8—1461no—
213C8—1462no—
214C22—21no—
215C22—21no—
216C22#1455656712yes—
217C22C22×C22⋊D7311yescharacteristic
218C4—22no—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—2921no—
224C4—2921no—
225C4—1464no—
226C4#1455656712yes—
227C4C2×Q8×D7311yescharacteristic
228C4C2×#1192402911yescharacteristic
229C2—22no—
230C2C2×#1455656711yescharacteristic
231C2#1798939811yescharacteristic
232C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#544×C73C2
socleC22×C73C22×D4
hypercenter#544D73
hypocenterC73#3082
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #17988891C2semidirect
3. #17988891C2semidirect
4. #17988879C2semidirect
5. #17988869C2semidirect
43. C2×Dic146Q8semidirect
117. C73#3082semidirect